We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least ℓ points, all of which have distinct colors. We give a 2-approximation to this problem for any ℓ when the objective is to minimize the maximum radius of any cluster. We show that the approximation ratio is optimal unless P=NP, by providing a matching lower bound. Several extensions to our algorithm have also been developed for handling outliers. This problem is mainly motivated by applications in privacy-preserving data publication.
@article{arxiv.1004.2968,
title = {Clustering with diversity},
author = {Jian Li and Ke Yi and Qin Zhang},
journal= {arXiv preprint arXiv:1004.2968},
year = {2010}
}